I am unfortunately running a later kernel, 4.8.4 in Fedora 24 Testing because I unsuccessfully fought an issue with running DisplayPort and HDMI. That was causing the entire system to lock up when the system went into suspend.

So anyway, in order to get this working you need to download the Ubuntu driver, execute it with extra flags and then install manually. It also requires to disable SELinux or if you have time and hair, figure out the profile to add so its happy.

# Run the following as root, your installing kernel modules etc
sudo su -
# Make sure you have kernel-devel
dnf install kernel-devel
# Disable SELinux till someone creates the relevant policy
setenforce 0
sed s/SELINUX=.*/SELINUX=disabled/ /etc/sysconfig/selinux
# Download the latest driver for Ubuntu
wget http://www.displaylink.com/downloads/file?id=708 -O 'DisplayLink USB Graphics Software for Ubuntu 1.2.1.zip'
# Unzip the driver
unzip 'DisplayLink USB Graphics Software for Ubuntu 1.2.1.zip'
# Make the .run script executable
chmod +x displaylink-driver-1.2.65.run
# Run the script with the noexec flag to prevent it from actually installing the driver
./displaylink-driver-1.2.65.run --noexec --keep
# Enter the directory
cd displaylink-driver-1.2.65
# Patch the displaylink-installer.sh with the patch from this gist
# It modifies the script to work with Fedora (Pretty naively...)
wget https://gist.githubusercontent.com/mattwilmott/d8893a24291f74975b6f2b48fa39fe24/raw/0cec3bbb2f1f21f806588d3cad57fbbdc5127c0a/displaylink-installer.sh.patch -O displaylink-installer.sh.patch
patch displaylink-installer.sh displaylink-installer.sh.patch
# Confirm the script is executable
chmod +x displaylink-installer.sh
# Install the driver
./displaylink-installer.sh install
# It should install without issue if it doesnt unfortunately your on your own. ;(
# Try rebooting and see if the screen works
# The displaylink service should now be active.
systemctl displaylink status
# If you ever need to remove it
# Backup the installer dir as it removes it AND your changes
tar -cjvf ../displaylink-installer.tgz ./
./displaylink-installer.sh uninstall